8,320 research outputs found
Analyzing shell structure from Babylonian and modern times
We investigate ``shell structure'' from Babylonian times: periodicities and
beats in computer-simulated lunar data corresponding to those observed by
Babylonian scribes some 2500 years ago. We discuss the mathematical similarity
between the Babylonians' recently reconstructed method of determining one of
the periods of the moon with modern Fourier analysis and the interpretation of
shell structure in finite fermion systems (nuclei, metal clusters, quantum
dots) in terms of classical closed or periodic orbits.Comment: LaTeX2e, 13pp, 8 figs; contribution to 10th Nuclear Physics Workshop
"Marie and Pierre Curie", 24 - 28 Sept. 2003, Kazimierz Dolny (Poland); final
version accepted for J. Mod. Phys.
Bifurcation cascades and self-similarity of periodic orbits with analytical scaling constants in Henon-Heiles type potentials
We investigate the isochronous bifurcations of the straight-line librating
orbit in the Henon-Heiles and related potentials. With increasing scaled energy
e, they form a cascade of pitchfork bifurcations that cumulate at the critical
saddle-point energy e=1. The stable and unstable orbits created at these
bifurcations appear in two sequences whose self-similar properties possess an
analytical scaling behavior. Different from the standard Feigenbaum scenario in
area preserving two-dimensional maps, here the scaling constants \alpha and
\beta corresponding to the two spatial directions are identical and equal to
the root of the scaling constant \delta that describes the geometric
progression of bifurcation energies e_n in the limit n --> infinity. The value
of \delta is given analytically in terms of the potential parameters.Comment: 20 pages, 10 figures, LaTeX. Contribution to Festschrift "To Martin
C. Gutzwiller on His Seventy-Fifth Birthday", eds. A. Inomata et al., final
revised version (updated references, note added in proof
Semiclassical description of shell effects in finite fermion systems
Since its first appearance in 1971, Gutzwiller's trace formula has been
extended to systems with continuous symmetries, in which not all periodic
orbits are isolated. In order to avoid the divergences occurring in connection
with symmetry breaking and orbit bifurcations (characteristic of systems with
mixed classical dynamics), special uniform approximations have been developed.
We first summarize some of the recent developments in this direction. Then we
present applications of the extended trace formulae to describe prominent
gross-shell effects of various finite fermion systems (atomic nuclei, metal
clusters, and a mesoscopic device) in terms of the leading periodic orbits of
their suitably modeled classical mean-field Hamiltonians.Comment: LaTeX, 12 pages, 9 figures; invited contribution to Symposium "30
Jahre Gutzwiller Spurformel" at DPG spring meeting, Hamburg, March 28, 2001.
To appear in Advances in Solid State Physic
Periodic orbit theory including spin degrees of freedom
We summarize recent developments of the semiclassical description of shell
effects in finite fermion systems with explicit inclusion of spin degrees of
freedom, in particluar in the presence of spin-orbit interactions. We present a
new approach that makes use of spin coherent states and a correspondingly
enlarged classical phase space. Taking suitable limits, we can recover some of
the earlier approaches. Applications to some model systems are presented.Comment: LaTeX2e, 10pp, 5 figs; contribution to 10th Nuclear Physics Workshop
"Marie and Pierre Curie", 24 - 28 Sept. 2003, Kazimierz Dolny (Poland
Supershell structure in trapped dilute Fermi gases
We show that a dilute harmonically trapped two-component gas of fermionic
atoms with a weak repulsive interaction has a pronounced super-shell structure:
the shell fillings due to the spherical harmonic trapping potential are
modulated by a beat mode. This changes the ``magic numbers'' occurring between
the beat nodes by half a period. The length and amplitude of this beating mode
depend on the strength of the interaction. We give a simple interpretation of
the beat structure in terms of a semiclassical trace formula for the symmetry
breaking U(3) --> SO(3).Comment: 4 pages, 4 figures; In version 2, references added. The semiclassical
explanation of super-shell structure is refined. Version 3, as appeared in
Phys. Rev.
Quantum fluid-dynamics from density functional theory
A partial differential eigenvalue equation for the density displacement
fields associated with electronic excitations is derived in the framework of
density functional theory. Our quantum fluid-dynamical approach is based on a
variational principle and the Kohn-Sham ground-state energy functional, using
only the occupied Kohn-Sham orbitals. It allows for an intuitive interpretation
of electronic excitations in terms of intrinsic local currents that obey a
continuity equation. We demonstrate the capabilities of this non-empirical
approach by calculating the photoabsorption spectra of small sodium clusters.
The quantitative agreement between theoretical and experimental spectra shows
that even for the smallest clusters, the resonances observed experimentally at
low temperatures can be interpreted in terms of density vibrations.Comment: RevTeX file with 2 figures. Update on April 17 2001: Typos corrected,
references updated, larger axes labels on Fig. 1. Accepted for publication in
Phys. Rev.
Closed-orbit theory for spatial density oscillations
We briefly review a recently developed semiclassical theory for quantum
oscillations in the spatial (particle and kinetic energy) densities of finite
fermion systems and present some examples of its results. We then discuss the
inclusion of correlations (finite temperatures, pairing correlations) in the
semiclassical theory.Comment: LaTeX, 10pp., 2 figure
Semiclassical analysis of the lowest-order multipole deformations of simple metal clusters
We use a perturbative semiclassical trace formula to calculate the three
lowest-order multipole (quadrupole \eps_2, octupole \eps_3, and
hexadecapole \eps_4) deformations of simple metal clusters with atoms in their ground states. The self-consistent mean field of the
valence electrons is modeled by an axially deformed cavity and the oscillating
part of the total energy is calculated semiclassically using the shortest
periodic orbits. The average energy is obtained from a liquid-drop model
adjusted to the empirical bulk and surface properties of the sodium metal. We
obtain good qualitative agreement with the results of quantum-mechanical
calculations using Strutinsky's shell-correction method.Comment: LaTeX file (v2) 6 figures, to be published in Phys. Lett.
- …